US 6859033 B2 Abstract A method for determining properties of a mixture of fluids includes: (a) acquiring a plurality of nuclear magnetic resonance measurements from the mixture of fluids, each of the plurality of nuclear magnetic resonance measurements having a different value in an acquisition parameter for which at least one relaxation selected from the group consisting of longitudinal relaxation and transverse relaxation affects magnitudes of the nuclear magnetic resonance measurements; (b) generating a model of the mixture of fluids; (c) calculating a synthesized nuclear magnetic data set based on the model; (d) comparing the synthesized nuclear magnetic data set with the nuclear magnetic resonance measurements; and (e) adjusting the model and repeating (c) and (d), if difference between the synthesized nuclear magnetic data set and the nuclear magnetic measurements is greater than a minimum.
Claims(25) 1. A method for determining properties of a mixture of fluids, comprising:
(a) acquiring a plurality of nuclear magnetic resonance measurements from the mixture of fluids, each of the plurality of nuclear magnetic resonance measurements having a different value in an acquisition parameter for which at least one relaxation selected from the group consisting of longitudinal relaxation and transverse relaxation affects magnitudes of the nuclear magnetic resonance measurements;
(b) generating a model of the mixture of fluids;
(c) calculating a synthesized nuclear magnetic data set based on model;
(d) comparing the synthesized nuclear magnetic data set with the nuclear magnetic resonance measurements; and
(e) adjusting the model and repeating (c) and (d), if difference between the synthesized nuclear magnetic data set and the nuclear magnetic measurements is greater than a minimum.
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A _{i} =A(1−S*e−RT/T _{1})e−ITE/T _{1 } where A is a full signal amplitude after full polarization along the static magnetic field, RT is an inversion recovery time in the inversion recovery sequence, TE is an inter-echo delay time in the Carr-Purcell-Meiboom-Gill sequence, T.sub.
1 is a longitudinal relaxation time, T.sub.2 is a transverse relaxation time, and S is define as:
S=1+IE*(1−e−WT/T _{1}). where IE is an inversion efficiency and WT is a polarization time.
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19. A method for logging an earth formation surrounding a wellbore, comprising:
(a) lowering a nuclear magnetic resonance instrument into the wellbore;
(b) inducing a static magnetic field in a region of investigation;
(c) generating a series of radio frequency magnetic field pulses in the region of investigation, and receiving signals comprising a train of nuclear magnetic resonance spin echoes in response to the series of radio frequency magnetic field pulses, wherein the generating and the receiving are repeated a plurality of times each with a different value in an acquisition parameter for which at least one of the longitudinal relaxation and transverse relaxation affects magnitudes of the signals;
(d) generating a formation model that includes at least one component for a connate water phase and at least one component for an oil phase, wherein the formation model comprises a set of amplitude components that define transverse relaxation time distribution of the connate water phase and a set of amplitude components that define transverse relaxation time distribution of the oil phase;
(e) calculating a synthesized nuclear magnetic data set based on the formation model;
(f) comparing the synthesized nuclear magnetic data set with the nuclear magnetic resonance measurements; and
(g) adjusting the formation model and repeating (c) and (d), if difference between the synthesized nuclear magnetic data set and the nuclear magnetic measurements is greater than a minimum.
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Description The invention relates generally to the field of well logging. More particularly, the invention relates to improved techniques for well logging using nuclear magnetic resonance and methods for analyzing the nuclear magnetic measurements. Oil well logging tools include nuclear magnetic resonance (NMR) instruments. NMR instruments can provide a wealth of information for formation evaluation that is not obtainable from other well logging measurements. Information provided by NMR measurements include the fractional volume of pore space, the fractional volume of mobile fluid filling the pore space, and the porosity of earth formations. General background of NMR well logging is described in U.S. Pat. No. 6,140,817A1, assigned to the assignee hereof. The signals measured by nuclear magnetic resonance (NMR) logging tools typically arise from the selected nuclei present in the probed volume. Because hydrogen nuclei are the most abundant and easily detectable, most NMR logging tools are tuned to detect hydrogen resonance signals (form either water or hydrocarbons). These hydrogen nuclei have different dynamic properties (e.g., diffusion rate and rotation rate) that are dependent on their environments. The different dynamic properties of these nuclei manifest themselves in different nuclear spin relaxation times (i.e., spin-lattice relaxation time (T Most NMR logging tools measure the spin-spin relaxation times (T Although T Recently, a magnetic resonance fluid characterization (MRF) method has been shown to provide more useful information. For a detailed discussion of the MRF method, see U.S. Pat. No. 6,229,308 B1 issued to Freedman and assigned to the assignee of the present invention. This patent is hereby incorporated by reference. When T While the MRF analysis has proved to be a powerful approach, it is desirable to have methods that can be used to analyze fluids with not only long T One aspect of the invention relates to methods for determining properties of a mixture of fluids using NMR data that include longitudinal and transverse relaxation information. According to embodiments of the invention, a method for determining properties of a mixture of fluids includes: (a) acquiring a plurality of nuclear magnetic resonance measurements from the mixture of fluids, each of the plurality of nuclear magnetic resonance measurements having a different value in an acquisition parameter for which at least one relaxation selected from the group consisting of longitudinal relaxation and transverse relaxation affects magnitudes of the nuclear magnetic resonance measurements; (b) generating a model of the mixture of fluids; (c) calculating a synthesized nuclear magnetic data set based on the model; (d) comparing the synthesized nuclear magnetic data set with the nuclear magnetic resonance measurements; and (e) adjusting the model and repeating (c) and (d), if difference between the synthesized nuclear magnetic data set and the nuclear magnetic measurements is greater than a minimum. Another aspect of the invention relates to methods for logging an earth formation surrounding a wellbore. According to embodiments of the invention, a method for logging an earth formation surrounding a wellbore includes: (a) lowering a nuclear magnetic resonance instrument into the wellbore; (b) inducing a static magnetic field in a region of investigation; (c) generating a series of radio frequency magnetic field pulses in the region of investigation, and receiving signals comprising a train of nuclear magnetic resonance spin echoes in response to the series of radio frequency magnetic field pulses, wherein the generating and the receiving are repeated a plurality of times each with a different value in an acquisition parameter for which at least one of the longitudinal relaxation and transverse relaxation affects magnitudes of the signals; (d) generating a formation model that includes at least one component for a connate water phase and at least one component for an oil phase; (e) calculating a synthesized nuclear magnetic data set based on the formation model; (f) comparing the synthesized nuclear magnetic data set with the nuclear magnetic resonance measurements; and (h) adjusting the formation model and repeating (c) and (d), if difference between the synthesized nuclear magnetic data set and the nuclear magnetic measurements is greater than a minimum. Other aspects and advantages of the invention will be apparent from the following description and the appended claims. The NMR logging tool A schematic representation of some of the components of an NMR logging tool Several NMR parameters may be measured that can be used to derive formation properties. Most NMR logging operations measure the spin-lattice (longitudinal) relaxation times (T Various pulse sequences are known in the art for measuring the NMR relaxation times. For example, T NMR measurements of diffusion constants are accomplished in the presence of magnetic field gradients. Magnetic field gradients produce different strengths of magnetic field at different locations. The different magnetic field strengths manifest themselves as different Larmor frequencies in the detected signals (because ω Once NMR data, which include information on T Freedman et al. disclosed a magnetic resonance fluid (MRF) characterization method that is capable of distinguishing different fluids even if they have overlapping NMR parameters (e.g., overlapping T The MRF method is based on two key concepts: (1) a new microscopic CVM (constituent viscosity model) that relates NMR relaxation times and molecular diffusion coefficients in crude oils, and (2) a new multi-fluid relaxation model. The MRF method provides a detailed formation evaluation of the near wellbore region investigated by modern NMR logging tools. The information provided by MRF includes flushed-zone fluid saturations and volumes, total and bound-fluid porosities, bulk volumes of hydrocarbon saturations, oil viscosities, and hydrocarbon-corrected permeabilities. CVM relates individual constituent diffusion-free relaxation times and diffusion coefficients to a distribution of constituent viscosities. The constituent viscosities are molecular variables that are analogous to the “friction coefficients” used in Langevin equation models of Brownian motion in viscous media. Before looking at the correlation between proton relaxation times and diffusion constants and the viscosity of a mixture, it is helpful to look at the simplest situation first, i.e., a pure liquid. In pure liquids, Bloembergen et al. in “ The dynamic properties of each individual constituent in a mixture are similar to those of a pure liquid. Thus, a similar relationship exists between the relaxation time (T The factor f(GOR) is included in equation (1) because it has been shown that GOR is an important parameter in determining the relaxation time dependence on viscosity and temperature. See Lo et al., Combining equations (1) and (2) provides the expression:
The validity of equations (1)-(4) has been shown (as disclosed in Freedman et al.) using experimental measurements of T The importance of the CVM for fluid characterization can be appreciated from equation (4), which correlates diffusion-free relaxation times with molecular diffusion in crude oils. This link reduces the number of unknown parameters in the NMR multifluid relaxation model and results in robust and accurate recovery of oil T The MRF method uses a general relaxation model for a formation containing brine, hydrocarbons, and oil-based mud filtrate (OBMF). Mud having hydrocarbons as the continuous phase is commonly used in drilling the borehole and it invades porous formations as OBMF. In the absence of magnetic field gradient or diffusion, the amplitudes of the spin echoes in NMR measurements decay exponentially as a function of time (T The apparent transverse (spin-spin) relaxations (T Similarly, the apparent transverse relaxation rates in the native oil
The measured viscosity (η The η The dependence of the relaxation times on viscosity and temperature in equations (8) and (9) is consistent with the experimental observations and theoretical predictions of Bloembergen, Purcell, and Pound, Similar to the Stokes-Einstein equation, the self-diffusion constants for the crude oils, D Analogously to the relationship between the macroscopic diffusion constant (D The MRF method inverts suites of NMR data using a multifluid relaxation model as shown in equation (5). In this model, different fluids that have overlapping T To use the contributions of differing molecular diffusion rates to resolve the fluid composition where there are overlapping T The suite of spin-echo measurements are then used in inversion analysis to fit the general multifluid relaxation model as shown in equation (5). Any inversion method known in the art may be used, including the Window Processing (WP) method disclosed in U.S. Pat. No. 5,291,137 issued to Freedman. This patent is assigned to the assignee of the present invention and is hereby incorporated by reference. For more detailed discussion of the MRF methods see Freedman et al., “ As stated above, for the diffusion constants to be measurable, the nuclear spin relaxing processes (longitudinal or transverse relaxation) should be slower than the diffusion process. Otherwise, the NMR signals would have diminished too much before any appreciable diffusion has occurred. In other words, if the NMR signal decays too quickly such that the decay becomes comparable with or faster than the signal decay due to the diffusion process, the diffusion constants can no longer be determined. Without the diffusion constants, the fluids with overlapping T The lower limits of T Embodiments of the present invention are capable of extending the applicability of the MRF method to situations where short NMR relaxation times do not permit accurate determination of the diffusion constants. Embodiments of the invention use other characteristics of the fluids, for example, different T In free fluids, T A T The T Using inversion recovery (IR) as an example, a pulse sequence for measuring the T In Ideally, WT in any pulse sequence should be long enough for all spins to relax back to the steady state (i.e., fully polarized by the static magnetic field) before the next pulse cycle. However, time economy often dictates that a shorter WT is used, which may result in incomplete magnetization being detected. If insufficient WT is used, polarization of the spins by the static magnetic field may not be complete. The detectable signal intensity under this condition is given by:
The measured signal amplitude (A The above formulation assumes that signal decay due to diffusion is negligible, and the measured spin echoes decay with true T Referring to curve (b) in According to equation (11), A For data inversion, if the T Once NMR data are collected, a formation model is generated (shown at The optimized formation model is then output (shown at The utility of embodiments of the present invention will now be illustrated with the following examples, in which computations are performed with a software package such as that sold under the trade name of MatLab™ by The MathWorks, Natick, Mass. First, two identical T
One pu of Gaussian noise was added to the experimental data. Then, 25 noise realizations were run for each suite. The data were then inverted using the nnls( ) function in MatLab™. This function provides an inversion with positivity constraint. The data were either inverted directly or with window sums. The window sums contained the following echoes: 1, 2-3, 4-6, 7-10, 11-16, 17-25, 26-39, 40-60, 61-91, 92-138, 139-208, 209-314, 315-500. The following tables show the results from the inversions (using “direct” or “window sums” (WS) approach):
These result show that the IR-CPMG suites (suites A comparison between results from suites The above simulation has assumed a T As shown in Because the results depend very sensitively on the T Instead of using a common T The above discussion presumes a homogeneous field. In an inhomogeneous field, the echo train decay constant may have contributions from both T Advantages of the present invention include its applicability to spins with short T The above discussion uses the T While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments can be devised without departing from the scope of the invention as disclosed herein. Accordingly, the scope of the invention should be limited only by the attached claims. Patent Citations
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